The Captain of a Spaceship Orbiting Planet X $( G = 6.67 \times$

Multiple Choice

The captain of a spaceship orbiting planet X discovers that to remain in orbit at 410 km from the planet's center, she needs to maintain a speed of 68 m/s . What is the mass of planet X? $( G = 6.67 \times$ $\left. 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $4.2 \times 10 ^ { 17 } \mathrm {~kg}$
B) $2.8 \times 10 ^ { 19 } \mathrm {~kg}$
C) $4.2 \times 10 ^ { 14 } \mathrm {~kg}$
D) $2.8 \times 10 ^ { 16 } \mathrm {~kg}$